Properties

Label 637.2.k.b.569.1
Level $637$
Weight $2$
Character 637.569
Analytic conductor $5.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.b.459.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+1.73205i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 + 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} -5.00000 q^{16} -6.00000 q^{17} +(-3.00000 + 1.73205i) q^{18} +(1.50000 - 0.866025i) q^{19} +(1.50000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 - 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-6.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{30} +(1.50000 - 0.866025i) q^{31} -5.19615i q^{32} +(4.50000 - 2.59808i) q^{33} -10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +(1.50000 + 2.59808i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(4.50000 + 2.59808i) q^{44} -3.46410i q^{45} +(-7.50000 - 4.33013i) q^{47} +(2.50000 - 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} -8.66025i q^{54} +(4.50000 + 7.79423i) q^{55} +1.73205i q^{57} +(4.50000 - 2.59808i) q^{58} +3.46410i q^{59} +(-1.50000 + 0.866025i) q^{60} +(3.50000 + 6.06218i) q^{61} +(1.50000 + 2.59808i) q^{62} -1.00000 q^{64} +(1.50000 - 6.06218i) q^{65} +(4.50000 + 7.79423i) q^{66} +(7.50000 + 4.33013i) q^{67} +6.00000 q^{68} +(1.50000 + 0.866025i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-7.50000 + 4.33013i) q^{73} +2.00000 q^{75} +(-1.50000 + 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +(7.50000 + 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} -3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +(-16.5000 - 9.52628i) q^{86} +3.00000 q^{87} +(4.50000 - 7.79423i) q^{88} -6.92820i q^{89} +6.00000 q^{90} +1.73205i q^{93} +(7.50000 - 12.9904i) q^{94} -3.00000 q^{95} +(4.50000 + 2.59808i) q^{96} +(4.50000 + 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 2q^{4} - 3q^{5} - 3q^{6} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} - 2q^{4} - 3q^{5} - 3q^{6} + 2q^{9} + 3q^{10} - 9q^{11} + q^{12} + 2q^{13} + 3q^{15} - 10q^{16} - 12q^{17} - 6q^{18} + 3q^{19} + 3q^{20} + 9q^{22} - 3q^{24} - 2q^{25} - 12q^{26} - 10q^{27} - 3q^{29} + 3q^{30} + 3q^{31} + 9q^{33} - 2q^{36} + 3q^{38} - 7q^{39} + 3q^{40} + 9q^{41} - 11q^{43} + 9q^{44} - 15q^{47} + 5q^{48} + 6q^{50} + 6q^{51} - 2q^{52} + 9q^{53} + 9q^{55} + 9q^{58} - 3q^{60} + 7q^{61} + 3q^{62} - 2q^{64} + 3q^{65} + 9q^{66} + 15q^{67} + 12q^{68} + 3q^{71} - 6q^{72} - 15q^{73} + 4q^{75} - 3q^{76} + 3q^{78} + 5q^{79} + 15q^{80} - q^{81} + 9q^{82} + 18q^{85} - 33q^{86} + 6q^{87} + 9q^{88} + 12q^{90} + 15q^{94} - 6q^{95} + 9q^{96} + 9q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i 0.790569 + 0.612372i \(0.209785\pi\)
−0.790569 + 0.612372i \(0.790215\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i \(-0.459925\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) −4.50000 2.59808i −1.35680 0.783349i −0.367610 0.929980i \(-0.619824\pi\)
−0.989191 + 0.146631i \(0.953157\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) 0 0
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) −5.00000 −1.25000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −3.00000 + 1.73205i −0.707107 + 0.408248i
\(19\) 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i \(-0.603001\pi\)
0.662094 + 0.749421i \(0.269668\pi\)
\(20\) 1.50000 + 0.866025i 0.335410 + 0.193649i
\(21\) 0 0
\(22\) 4.50000 7.79423i 0.959403 1.66174i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) −6.00000 + 1.73205i −1.17670 + 0.339683i
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 1.50000 0.866025i 0.269408 0.155543i −0.359211 0.933257i \(-0.616954\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 5.19615i 0.918559i
\(33\) 4.50000 2.59808i 0.783349 0.452267i
\(34\) 10.3923i 1.78227i
\(35\) 0 0
\(36\) −1.00000 1.73205i −0.166667 0.288675i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 1.50000 + 2.59808i 0.243332 + 0.421464i
\(39\) −3.50000 0.866025i −0.560449 0.138675i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 4.50000 2.59808i 0.702782 0.405751i −0.105601 0.994409i \(-0.533677\pi\)
0.808383 + 0.588657i \(0.200343\pi\)
\(42\) 0 0
\(43\) −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i \(0.483375\pi\)
−0.890947 + 0.454108i \(0.849958\pi\)
\(44\) 4.50000 + 2.59808i 0.678401 + 0.391675i
\(45\) 3.46410i 0.516398i
\(46\) 0 0
\(47\) −7.50000 4.33013i −1.09399 0.631614i −0.159352 0.987222i \(-0.550941\pi\)
−0.934635 + 0.355608i \(0.884274\pi\)
\(48\) 2.50000 4.33013i 0.360844 0.625000i
\(49\) 0 0
\(50\) 3.00000 1.73205i 0.424264 0.244949i
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) −1.00000 3.46410i −0.138675 0.480384i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 8.66025i 1.17851i
\(55\) 4.50000 + 7.79423i 0.606780 + 1.05097i
\(56\) 0 0
\(57\) 1.73205i 0.229416i
\(58\) 4.50000 2.59808i 0.590879 0.341144i
\(59\) 3.46410i 0.450988i 0.974245 + 0.225494i \(0.0723995\pi\)
−0.974245 + 0.225494i \(0.927600\pi\)
\(60\) −1.50000 + 0.866025i −0.193649 + 0.111803i
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 1.50000 + 2.59808i 0.190500 + 0.329956i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.50000 6.06218i 0.186052 0.751921i
\(66\) 4.50000 + 7.79423i 0.553912 + 0.959403i
\(67\) 7.50000 + 4.33013i 0.916271 + 0.529009i 0.882443 0.470418i \(-0.155897\pi\)
0.0338274 + 0.999428i \(0.489230\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) 1.50000 + 0.866025i 0.178017 + 0.102778i 0.586361 0.810050i \(-0.300560\pi\)
−0.408344 + 0.912828i \(0.633893\pi\)
\(72\) −3.00000 + 1.73205i −0.353553 + 0.204124i
\(73\) −7.50000 + 4.33013i −0.877809 + 0.506803i −0.869935 0.493166i \(-0.835840\pi\)
−0.00787336 + 0.999969i \(0.502506\pi\)
\(74\) 0 0
\(75\) 2.00000 0.230940
\(76\) −1.50000 + 0.866025i −0.172062 + 0.0993399i
\(77\) 0 0
\(78\) 1.50000 6.06218i 0.169842 0.686406i
\(79\) 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i \(-0.742577\pi\)
0.971698 + 0.236225i \(0.0759104\pi\)
\(80\) 7.50000 + 4.33013i 0.838525 + 0.484123i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.50000 + 7.79423i 0.496942 + 0.860729i
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) 0 0
\(85\) 9.00000 + 5.19615i 0.976187 + 0.563602i
\(86\) −16.5000 9.52628i −1.77924 1.02725i
\(87\) 3.00000 0.321634
\(88\) 4.50000 7.79423i 0.479702 0.830868i
\(89\) 6.92820i 0.734388i −0.930144 0.367194i \(-0.880318\pi\)
0.930144 0.367194i \(-0.119682\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) 0 0
\(93\) 1.73205i 0.179605i
\(94\) 7.50000 12.9904i 0.773566 1.33986i
\(95\) −3.00000 −0.307794
\(96\) 4.50000 + 2.59808i 0.459279 + 0.265165i
\(97\) 4.50000 + 2.59808i 0.456906 + 0.263795i 0.710742 0.703452i \(-0.248359\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 0 0
\(99\) 10.3923i 1.04447i
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 9.00000 + 5.19615i 0.891133 + 0.514496i
\(103\) −6.50000 + 11.2583i −0.640464 + 1.10932i 0.344865 + 0.938652i \(0.387925\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) −6.00000 + 1.73205i −0.588348 + 0.169842i
\(105\) 0 0
\(106\) −13.5000 + 7.79423i −1.31124 + 0.757042i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 5.00000 0.481125
\(109\) −4.50000 + 2.59808i −0.431022 + 0.248851i −0.699782 0.714357i \(-0.746719\pi\)
0.268760 + 0.963207i \(0.413386\pi\)
\(110\) −13.5000 + 7.79423i −1.28717 + 0.743151i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) −3.00000 −0.280976
\(115\) 0 0
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) −5.00000 + 5.19615i −0.462250 + 0.480384i
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) 8.00000 + 13.8564i 0.727273 + 1.25967i
\(122\) −10.5000 + 6.06218i −0.950625 + 0.548844i
\(123\) 5.19615i 0.468521i
\(124\) −1.50000 + 0.866025i −0.134704 + 0.0777714i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) −6.50000 11.2583i −0.576782 0.999015i −0.995846 0.0910585i \(-0.970975\pi\)
0.419064 0.907957i \(-0.362358\pi\)
\(128\) 12.1244i 1.07165i
\(129\) −5.50000 9.52628i −0.484248 0.838742i
\(130\) 10.5000 + 2.59808i 0.920911 + 0.227866i
\(131\) 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i \(-0.605885\pi\)
0.981824 0.189794i \(-0.0607819\pi\)
\(132\) −4.50000 + 2.59808i −0.391675 + 0.226134i
\(133\) 0 0
\(134\) −7.50000 + 12.9904i −0.647901 + 1.12220i
\(135\) 7.50000 + 4.33013i 0.645497 + 0.372678i
\(136\) 10.3923i 0.891133i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i \(0.352543\pi\)
−0.998179 + 0.0603135i \(0.980790\pi\)
\(140\) 0 0
\(141\) 7.50000 4.33013i 0.631614 0.364662i
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) 4.50000 18.1865i 0.376309 1.52083i
\(144\) −5.00000 8.66025i −0.416667 0.721688i
\(145\) 5.19615i 0.431517i
\(146\) −7.50000 12.9904i −0.620704 1.07509i
\(147\) 0 0
\(148\) 0 0
\(149\) −16.5000 + 9.52628i −1.35173 + 0.780423i −0.988492 0.151272i \(-0.951663\pi\)
−0.363241 + 0.931695i \(0.618330\pi\)
\(150\) 3.46410i 0.282843i
\(151\) 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i \(-0.502445\pi\)
0.862159 + 0.506637i \(0.169112\pi\)
\(152\) 1.50000 + 2.59808i 0.121666 + 0.210732i
\(153\) −6.00000 10.3923i −0.485071 0.840168i
\(154\) 0 0
\(155\) −3.00000 −0.240966
\(156\) 3.50000 + 0.866025i 0.280224 + 0.0693375i
\(157\) 11.5000 + 19.9186i 0.917800 + 1.58968i 0.802749 + 0.596316i \(0.203370\pi\)
0.115050 + 0.993360i \(0.463297\pi\)
\(158\) 7.50000 + 4.33013i 0.596668 + 0.344486i
\(159\) −9.00000 −0.713746
\(160\) −4.50000 + 7.79423i −0.355756 + 0.616188i
\(161\) 0 0
\(162\) −1.50000 0.866025i −0.117851 0.0680414i
\(163\) 10.5000 6.06218i 0.822423 0.474826i −0.0288280 0.999584i \(-0.509178\pi\)
0.851251 + 0.524758i \(0.175844\pi\)
\(164\) −4.50000 + 2.59808i −0.351391 + 0.202876i
\(165\) −9.00000 −0.700649
\(166\) 6.00000 0.465690
\(167\) 1.50000 0.866025i 0.116073 0.0670151i −0.440839 0.897586i \(-0.645319\pi\)
0.556913 + 0.830571i \(0.311986\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) −9.00000 + 15.5885i −0.690268 + 1.19558i
\(171\) 3.00000 + 1.73205i 0.229416 + 0.132453i
\(172\) 5.50000 9.52628i 0.419371 0.726372i
\(173\) 7.50000 + 12.9904i 0.570214 + 0.987640i 0.996544 + 0.0830722i \(0.0264732\pi\)
−0.426329 + 0.904568i \(0.640193\pi\)
\(174\) 5.19615i 0.393919i
\(175\) 0 0
\(176\) 22.5000 + 12.9904i 1.69600 + 0.979187i
\(177\) −3.00000 1.73205i −0.225494 0.130189i
\(178\) 12.0000 0.899438
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 3.46410i 0.258199i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) 0 0
\(185\) 0 0
\(186\) −3.00000 −0.219971
\(187\) 27.0000 + 15.5885i 1.97444 + 1.13994i
\(188\) 7.50000 + 4.33013i 0.546994 + 0.315807i
\(189\) 0 0
\(190\) 5.19615i 0.376969i
\(191\) 7.50000 + 12.9904i 0.542681 + 0.939951i 0.998749 + 0.0500060i \(0.0159241\pi\)
−0.456068 + 0.889945i \(0.650743\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 1.50000 + 0.866025i 0.107972 + 0.0623379i 0.553014 0.833172i \(-0.313478\pi\)
−0.445041 + 0.895510i \(0.646811\pi\)
\(194\) −4.50000 + 7.79423i −0.323081 + 0.559593i
\(195\) 4.50000 + 4.33013i 0.322252 + 0.310087i
\(196\) 0 0
\(197\) 19.5000 11.2583i 1.38932 0.802123i 0.396079 0.918216i \(-0.370371\pi\)
0.993238 + 0.116094i \(0.0370372\pi\)
\(198\) 18.0000 1.27920
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 3.00000 1.73205i 0.212132 0.122474i
\(201\) −7.50000 + 4.33013i −0.529009 + 0.305424i
\(202\) −13.5000 7.79423i −0.949857 0.548400i
\(203\) 0 0
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) −9.00000 −0.628587
\(206\) −19.5000 11.2583i −1.35863 0.784405i
\(207\) 0 0
\(208\) −5.00000 17.3205i −0.346688 1.20096i
\(209\) −9.00000 −0.622543
\(210\) 0 0
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) −1.50000 + 0.866025i −0.102778 + 0.0593391i
\(214\) 0 0
\(215\) 16.5000 9.52628i 1.12529 0.649687i
\(216\) 8.66025i 0.589256i
\(217\) 0 0
\(218\) −4.50000 7.79423i −0.304778 0.527892i
\(219\) 8.66025i 0.585206i
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) −6.00000 20.7846i −0.403604 1.39812i
\(222\) 0 0
\(223\) −4.50000 + 2.59808i −0.301342 + 0.173980i −0.643046 0.765828i \(-0.722329\pi\)
0.341703 + 0.939808i \(0.388996\pi\)
\(224\) 0 0
\(225\) 2.00000 3.46410i 0.133333 0.230940i
\(226\) −22.5000 12.9904i −1.49668 0.864107i
\(227\) 17.3205i 1.14960i 0.818293 + 0.574801i \(0.194921\pi\)
−0.818293 + 0.574801i \(0.805079\pi\)
\(228\) 1.73205i 0.114708i
\(229\) 10.5000 + 6.06218i 0.693860 + 0.400600i 0.805056 0.593198i \(-0.202135\pi\)
−0.111197 + 0.993798i \(0.535468\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.50000 2.59808i 0.295439 0.170572i
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) −9.00000 8.66025i −0.588348 0.566139i
\(235\) 7.50000 + 12.9904i 0.489246 + 0.847399i
\(236\) 3.46410i 0.225494i
\(237\) 2.50000 + 4.33013i 0.162392 + 0.281272i
\(238\) 0 0
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) −7.50000 + 4.33013i −0.484123 + 0.279508i
\(241\) 6.92820i 0.446285i 0.974786 + 0.223142i \(0.0716315\pi\)
−0.974786 + 0.223142i \(0.928369\pi\)
\(242\) −24.0000 + 13.8564i −1.54278 + 0.890724i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −3.50000 6.06218i −0.224065 0.388091i
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) 4.50000 + 4.33013i 0.286328 + 0.275519i
\(248\) 1.50000 + 2.59808i 0.0952501 + 0.164978i
\(249\) 3.00000 + 1.73205i 0.190117 + 0.109764i
\(250\) −21.0000 −1.32816
\(251\) 1.50000 2.59808i 0.0946792 0.163989i −0.814795 0.579748i \(-0.803151\pi\)
0.909475 + 0.415759i \(0.136484\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 19.5000 11.2583i 1.22354 0.706410i
\(255\) −9.00000 + 5.19615i −0.563602 + 0.325396i
\(256\) 19.0000 1.18750
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) 16.5000 9.52628i 1.02725 0.593080i
\(259\) 0 0
\(260\) −1.50000 + 6.06218i −0.0930261 + 0.375960i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 22.5000 + 12.9904i 1.39005 + 0.802548i
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) 4.50000 + 7.79423i 0.276956 + 0.479702i
\(265\) 15.5885i 0.957591i
\(266\) 0 0
\(267\) 6.00000 + 3.46410i 0.367194 + 0.212000i
\(268\) −7.50000 4.33013i −0.458135 0.264505i
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −7.50000 + 12.9904i −0.456435 + 0.790569i
\(271\) 17.3205i 1.05215i −0.850439 0.526073i \(-0.823664\pi\)
0.850439 0.526073i \(-0.176336\pi\)
\(272\) 30.0000 1.81902
\(273\) 0 0
\(274\) 0 0
\(275\) 10.3923i 0.626680i
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −19.5000 11.2583i −1.16953 0.675230i
\(279\) 3.00000 + 1.73205i 0.179605 + 0.103695i
\(280\) 0 0
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) 7.50000 + 12.9904i 0.446619 + 0.773566i
\(283\) 9.50000 16.4545i 0.564716 0.978117i −0.432360 0.901701i \(-0.642319\pi\)
0.997076 0.0764162i \(-0.0243478\pi\)
\(284\) −1.50000 0.866025i −0.0890086 0.0513892i
\(285\) 1.50000 2.59808i 0.0888523 0.153897i
\(286\) 31.5000 + 7.79423i 1.86263 + 0.460882i
\(287\) 0 0
\(288\) 9.00000 5.19615i 0.530330 0.306186i
\(289\) 19.0000 1.11765
\(290\) −9.00000 −0.528498
\(291\) −4.50000 + 2.59808i −0.263795 + 0.152302i
\(292\) 7.50000 4.33013i 0.438904 0.253402i
\(293\) 22.5000 + 12.9904i 1.31446 + 0.758906i 0.982832 0.184503i \(-0.0590674\pi\)
0.331632 + 0.943409i \(0.392401\pi\)
\(294\) 0 0
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) 0 0
\(297\) 22.5000 + 12.9904i 1.30558 + 0.753778i
\(298\) −16.5000 28.5788i −0.955819 1.65553i
\(299\) 0 0
\(300\) −2.00000 −0.115470
\(301\) 0 0
\(302\) 10.5000 + 18.1865i 0.604207 + 1.04652i
\(303\) −4.50000 7.79423i −0.258518 0.447767i
\(304\) −7.50000 + 4.33013i −0.430155 + 0.248350i
\(305\) 12.1244i 0.694239i
\(306\) 18.0000 10.3923i 1.02899 0.594089i
\(307\) 24.2487i 1.38395i −0.721923 0.691974i \(-0.756741\pi\)
0.721923 0.691974i \(-0.243259\pi\)
\(308\) 0 0
\(309\) −6.50000 11.2583i −0.369772 0.640464i
\(310\) 5.19615i 0.295122i
\(311\) −7.50000 12.9904i −0.425286 0.736617i 0.571161 0.820838i \(-0.306493\pi\)
−0.996447 + 0.0842210i \(0.973160\pi\)
\(312\) 1.50000 6.06218i 0.0849208 0.343203i
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) −34.5000 + 19.9186i −1.94695 + 1.12407i
\(315\) 0 0
\(316\) −2.50000 + 4.33013i −0.140636 + 0.243589i
\(317\) −4.50000 2.59808i −0.252745 0.145922i 0.368275 0.929717i \(-0.379948\pi\)
−0.621021 + 0.783794i \(0.713282\pi\)
\(318\) 15.5885i 0.874157i
\(319\) 15.5885i 0.872786i
\(320\) 1.50000 + 0.866025i 0.0838525 + 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) −9.00000 + 5.19615i −0.500773 + 0.289122i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 5.00000 5.19615i 0.277350 0.288231i
\(326\) 10.5000 + 18.1865i 0.581541 + 1.00726i
\(327\) 5.19615i 0.287348i
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 15.5885i 0.858116i
\(331\) 28.5000 16.4545i 1.56650 0.904420i 0.569929 0.821694i \(-0.306971\pi\)
0.996572 0.0827265i \(-0.0263628\pi\)
\(332\) 3.46410i 0.190117i
\(333\) 0 0
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) −7.50000 12.9904i −0.409769 0.709740i
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) −12.0000 19.0526i −0.652714 1.03632i
\(339\) −7.50000 12.9904i −0.407344 0.705541i
\(340\) −9.00000 5.19615i −0.488094 0.281801i
\(341\) −9.00000 −0.487377
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 0 0
\(344\) −16.5000 9.52628i −0.889620 0.513623i
\(345\) 0 0
\(346\) −22.5000 + 12.9904i −1.20961 + 0.698367i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) −3.00000 −0.160817
\(349\) 4.50000 2.59808i 0.240879 0.139072i −0.374701 0.927146i \(-0.622255\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 0 0
\(351\) −5.00000 17.3205i −0.266880 0.924500i
\(352\) −13.5000 + 23.3827i −0.719552 + 1.24630i
\(353\) −1.50000 0.866025i −0.0798369 0.0460939i 0.459550 0.888152i \(-0.348011\pi\)
−0.539387 + 0.842058i \(0.681344\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) −1.50000 2.59808i −0.0796117 0.137892i
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) −4.50000 2.59808i −0.237832 0.137313i
\(359\) −16.5000 9.52628i −0.870837 0.502778i −0.00321050 0.999995i \(-0.501022\pi\)
−0.867626 + 0.497217i \(0.834355\pi\)
\(360\) 6.00000 0.316228
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 3.46410i 0.182069i
\(363\) −16.0000 −0.839782
\(364\) 0 0
\(365\) 15.0000 0.785136
\(366\) 12.1244i 0.633750i
\(367\) 11.5000 19.9186i 0.600295 1.03974i −0.392481 0.919760i \(-0.628383\pi\)
0.992776 0.119982i \(-0.0382835\pi\)
\(368\) 0 0
\(369\) 9.00000 + 5.19615i 0.468521 + 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 1.73205i 0.0898027i
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) −27.0000 + 46.7654i −1.39614 + 2.41818i
\(375\) −10.5000 6.06218i −0.542218 0.313050i
\(376\) 7.50000 12.9904i 0.386783 0.669928i
\(377\) 7.50000 7.79423i 0.386270 0.401423i
\(378\) 0 0
\(379\) −1.50000 + 0.866025i −0.0770498 + 0.0444847i −0.538030 0.842926i \(-0.680831\pi\)
0.460980 + 0.887410i \(0.347498\pi\)
\(380\) 3.00000 0.153897
\(381\) 13.0000 0.666010
\(382\) −22.5000 + 12.9904i −1.15120 + 0.664646i
\(383\) 13.5000 7.79423i 0.689818 0.398266i −0.113726 0.993512i \(-0.536279\pi\)
0.803544 + 0.595246i \(0.202945\pi\)
\(384\) 10.5000 + 6.06218i 0.535826 + 0.309359i
\(385\) 0 0
\(386\) −1.50000 + 2.59808i −0.0763480 + 0.132239i
\(387\) −22.0000 −1.11832
\(388\) −4.50000 2.59808i −0.228453 0.131897i
\(389\) −1.50000 2.59808i −0.0760530 0.131728i 0.825491 0.564416i \(-0.190898\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(390\) −7.50000 + 7.79423i −0.379777 + 0.394676i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 19.5000 + 33.7750i 0.982396 + 1.70156i
\(395\) −7.50000 + 4.33013i −0.377366 + 0.217872i
\(396\) 10.3923i 0.522233i
\(397\) −31.5000 + 18.1865i −1.58094 + 0.912756i −0.586217 + 0.810154i \(0.699383\pi\)
−0.994722 + 0.102602i \(0.967283\pi\)
\(398\) 6.92820i 0.347279i
\(399\) 0 0
\(400\) 5.00000 + 8.66025i 0.250000 + 0.433013i
\(401\) 6.92820i 0.345978i 0.984924 + 0.172989i \(0.0553425\pi\)
−0.984924 + 0.172989i \(0.944657\pi\)
\(402\) −7.50000 12.9904i −0.374066 0.647901i
\(403\) 4.50000 + 4.33013i 0.224161 + 0.215699i
\(404\) 4.50000 7.79423i 0.223883 0.387777i
\(405\) 1.50000 0.866025i 0.0745356 0.0430331i
\(406\) 0 0
\(407\) 0 0
\(408\) 9.00000 + 5.19615i 0.445566 + 0.257248i
\(409\) 6.92820i 0.342578i −0.985221 0.171289i \(-0.945207\pi\)
0.985221 0.171289i \(-0.0547931\pi\)
\(410\) 15.5885i 0.769859i
\(411\) 0 0
\(412\) 6.50000 11.2583i 0.320232 0.554658i
\(413\) 0 0
\(414\) 0 0
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) 18.0000 5.19615i 0.882523 0.254762i
\(417\) −6.50000 11.2583i −0.318306 0.551323i
\(418\) 15.5885i 0.762456i
\(419\) 10.5000 + 18.1865i 0.512959 + 0.888470i 0.999887 + 0.0150285i \(0.00478389\pi\)
−0.486928 + 0.873442i \(0.661883\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 19.5000 11.2583i 0.949245 0.548047i
\(423\) 17.3205i 0.842152i
\(424\) −13.5000 + 7.79423i −0.655618 + 0.378521i
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) −1.50000 2.59808i −0.0726752 0.125877i
\(427\) 0 0
\(428\) 0 0
\(429\) 13.5000 + 12.9904i 0.651786 + 0.627182i
\(430\) 16.5000 + 28.5788i 0.795701 + 1.37819i
\(431\) −28.5000 16.4545i −1.37280 0.792585i −0.381517 0.924362i \(-0.624598\pi\)
−0.991279 + 0.131777i \(0.957932\pi\)
\(432\) 25.0000 1.20281
\(433\) 9.50000 16.4545i 0.456541 0.790752i −0.542234 0.840227i \(-0.682422\pi\)
0.998775 + 0.0494752i \(0.0157549\pi\)
\(434\) 0 0
\(435\) −4.50000 2.59808i −0.215758 0.124568i
\(436\) 4.50000 2.59808i 0.215511 0.124425i
\(437\) 0 0
\(438\) 15.0000 0.716728
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) −13.5000 + 7.79423i −0.643587 + 0.371575i
\(441\) 0 0
\(442\) 36.0000 10.3923i 1.71235 0.494312i
\(443\) −7.50000 + 12.9904i −0.356336 + 0.617192i −0.987346 0.158583i \(-0.949307\pi\)
0.631010 + 0.775775i \(0.282641\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −4.50000 7.79423i −0.213081 0.369067i
\(447\) 19.0526i 0.901155i
\(448\) 0 0
\(449\) 1.50000 + 0.866025i 0.0707894 + 0.0408703i 0.534977 0.844867i \(-0.320320\pi\)
−0.464188 + 0.885737i \(0.653654\pi\)
\(450\) 6.00000 + 3.46410i 0.282843 + 0.163299i
\(451\) −27.0000 −1.27138
\(452\) 7.50000 12.9904i 0.352770 0.611016i
\(453\) 12.1244i 0.569652i
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 34.6410i 1.62044i 0.586127 + 0.810219i \(0.300652\pi\)
−0.586127 + 0.810219i \(0.699348\pi\)
\(458\) −10.5000 + 18.1865i −0.490633 + 0.849801i
\(459\) 30.0000 1.40028
\(460\) 0 0
\(461\) −25.5000 14.7224i −1.18765 0.685692i −0.229881 0.973219i \(-0.573834\pi\)
−0.957773 + 0.287527i \(0.907167\pi\)
\(462\) 0 0
\(463\) 24.2487i 1.12693i −0.826139 0.563467i \(-0.809467\pi\)
0.826139 0.563467i \(-0.190533\pi\)
\(464\) 7.50000 + 12.9904i 0.348179 + 0.603063i
\(465\) 1.50000 2.59808i 0.0695608 0.120483i
\(466\) −4.50000 2.59808i −0.208458 0.120354i
\(467\) −10.5000 + 18.1865i −0.485882 + 0.841572i −0.999868 0.0162260i \(-0.994835\pi\)
0.513986 + 0.857798i \(0.328168\pi\)
\(468\) 5.00000 5.19615i 0.231125 0.240192i
\(469\) 0 0
\(470\) −22.5000 + 12.9904i −1.03785 + 0.599202i
\(471\) −23.0000 −1.05978
\(472\) −6.00000 −0.276172
\(473\) 49.5000 28.5788i 2.27601 1.31406i
\(474\) −7.50000 + 4.33013i −0.344486 + 0.198889i
\(475\) −3.00000 1.73205i −0.137649 0.0794719i
\(476\) 0 0
\(477\) −9.00000 + 15.5885i −0.412082 + 0.713746i
\(478\) −18.0000 −0.823301
\(479\) −25.5000 14.7224i −1.16512 0.672685i −0.212598 0.977140i \(-0.568192\pi\)
−0.952527 + 0.304455i \(0.901526\pi\)
\(480\) −4.50000 7.79423i −0.205396 0.355756i
\(481\) 0 0
\(482\) −12.0000 −0.546585
\(483\) 0 0
\(484\) −8.00000 13.8564i −0.363636 0.629837i
\(485\) −4.50000 7.79423i −0.204334 0.353918i
\(486\) 24.0000 13.8564i 1.08866 0.628539i
\(487\) 24.2487i 1.09881i −0.835555 0.549407i \(-0.814854\pi\)
0.835555 0.549407i \(-0.185146\pi\)
\(488\) −10.5000 + 6.06218i −0.475313 + 0.274422i
\(489\) 12.1244i 0.548282i
\(490\) 0 0
\(491\) 13.5000 + 23.3827i 0.609246 + 1.05525i 0.991365 + 0.131132i \(0.0418613\pi\)
−0.382118 + 0.924113i \(0.624805\pi\)
\(492\) 5.19615i 0.234261i
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) −7.50000 + 7.79423i −0.337441 + 0.350679i
\(495\) −9.00000 + 15.5885i −0.404520 + 0.700649i
\(496\) −7.50000 + 4.33013i −0.336760 + 0.194428i
\(497\) 0 0
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 1.50000 + 0.866025i 0.0671492 + 0.0387686i 0.533199 0.845990i \(-0.320990\pi\)
−0.466049 + 0.884759i \(0.654323\pi\)
\(500\) 12.1244i 0.542218i
\(501\) 1.73205i 0.0773823i
\(502\) 4.50000 + 2.59808i 0.200845 + 0.115958i
\(503\) −4.50000 + 7.79423i −0.200645 + 0.347527i −0.948736 0.316068i \(-0.897637\pi\)
0.748091 + 0.663596i \(0.230970\pi\)
\(504\) 0 0
\(505\) 13.5000 7.79423i 0.600742 0.346839i
\(506\) 0 0
\(507\) −0.500000 12.9904i −0.0222058 0.576923i
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 6.92820i 0.307087i −0.988142 0.153544i \(-0.950931\pi\)
0.988142 0.153544i \(-0.0490686\pi\)
\(510\) −9.00000 15.5885i −0.398527 0.690268i
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) −7.50000 + 4.33013i −0.331133 + 0.191180i
\(514\) 51.9615i 2.29192i
\(515\) 19.5000 11.2583i 0.859273 0.496101i
\(516\) 5.50000 + 9.52628i 0.242124 + 0.419371i
\(517\) 22.5000 + 38.9711i 0.989549 + 1.71395i
\(518\) 0 0
\(519\) −15.0000 −0.658427
\(520\) 10.5000 + 2.59808i 0.460455 + 0.113933i
\(521\) 19.5000 + 33.7750i 0.854311 + 1.47971i 0.877283 + 0.479973i \(0.159354\pi\)
−0.0229727 + 0.999736i \(0.507313\pi\)
\(522\) 9.00000 + 5.19615i 0.393919 + 0.227429i
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) −4.50000 2.59808i −0.196209 0.113282i
\(527\) −9.00000 + 5.19615i −0.392046 + 0.226348i
\(528\) −22.5000 + 12.9904i −0.979187 + 0.565334i
\(529\) −23.0000 −1.00000
\(530\) 27.0000 1.17281
\(531\) −6.00000 + 3.46410i −0.260378 + 0.150329i
\(532\) 0 0
\(533\) 13.5000 + 12.9904i 0.584750 + 0.562676i
\(534\) −6.00000 + 10.3923i −0.259645 + 0.449719i
\(535\) 0 0
\(536\) −7.50000 + 12.9904i −0.323951 + 0.561099i
\(537\) −1.50000 2.59808i −0.0647298 0.112115i
\(538\) 10.3923i 0.448044i
\(539\) 0 0
\(540\) −7.50000 4.33013i −0.322749 0.186339i
\(541\) −10.5000 6.06218i −0.451430 0.260633i 0.257004 0.966410i \(-0.417265\pi\)
−0.708434 + 0.705777i \(0.750598\pi\)
\(542\) 30.0000 1.28861
\(543\) 1.00000 1.73205i 0.0429141 0.0743294i
\(544\) 31.1769i 1.33670i
\(545\) 9.00000 0.385518
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) −7.00000 + 12.1244i −0.298753 + 0.517455i
\(550\) −18.0000 −0.767523
\(551\) −4.50000 2.59808i −0.191706 0.110682i
\(552\) 0 0
\(553\) 0 0
\(554\) 17.3205i 0.735878i
\(555\) 0 0
\(556\) 6.50000 11.2583i 0.275661 0.477460i
\(557\) 13.5000 + 7.79423i 0.572013 + 0.330252i 0.757953 0.652309i \(-0.226200\pi\)
−0.185940 + 0.982561i \(0.559533\pi\)
\(558\) −3.00000 + 5.19615i −0.127000 + 0.219971i
\(559\) −38.5000 9.52628i −1.62838 0.402919i
\(560\) 0 0
\(561\) −27.0000 + 15.5885i −1.13994 + 0.658145i
\(562\) 12.0000 0.506189
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) −7.50000 + 4.33013i −0.315807 + 0.182331i
\(565\) 22.5000 12.9904i 0.946582 0.546509i
\(566\) 28.5000 + 16.4545i 1.19794 + 0.691633i
\(567\) 0 0
\(568\) −1.50000 + 2.59808i −0.0629386 + 0.109013i
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 4.50000 + 2.59808i 0.188484 + 0.108821i
\(571\) 11.5000 + 19.9186i 0.481260 + 0.833567i 0.999769 0.0215055i \(-0.00684595\pi\)
−0.518509 + 0.855072i \(0.673513\pi\)
\(572\) −4.50000 + 18.1865i −0.188154 + 0.760417i
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) 0 0
\(576\) −1.00000 1.73205i −0.0416667 0.0721688i
\(577\) −13.5000 + 7.79423i −0.562012 + 0.324478i −0.753953 0.656929i \(-0.771855\pi\)
0.191940 + 0.981407i \(0.438522\pi\)
\(578\) 32.9090i 1.36883i
\(579\) −1.50000 + 0.866025i −0.0623379 + 0.0359908i
\(580\) 5.19615i 0.215758i
\(581\) 0 0
\(582\) −4.50000 7.79423i −0.186531 0.323081i
\(583\) 46.7654i 1.93682i
\(584\) −7.50000 12.9904i −0.310352 0.537546i
\(585\) 12.0000 3.46410i 0.496139 0.143223i
\(586\) −22.5000 + 38.9711i −0.929466 + 1.60988i
\(587\) 13.5000 7.79423i 0.557205 0.321702i −0.194818 0.980839i \(-0.562412\pi\)
0.752023 + 0.659137i \(0.229078\pi\)
\(588\) 0 0
\(589\) 1.50000 2.59808i 0.0618064 0.107052i
\(590\) 9.00000 + 5.19615i 0.370524 + 0.213922i
\(591\) 22.5167i 0.926212i
\(592\) 0 0
\(593\) 4.50000 + 2.59808i 0.184793 + 0.106690i 0.589543 0.807737i \(-0.299308\pi\)
−0.404750 + 0.914428i \(0.632641\pi\)
\(594\) −22.5000 + 38.9711i −0.923186 + 1.59901i
\(595\) 0 0
\(596\) 16.5000 9.52628i 0.675866 0.390212i
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 0 0
\(599\) −4.50000 7.79423i −0.183865 0.318464i 0.759328 0.650708i \(-0.225528\pi\)
−0.943193 + 0.332244i \(0.892194\pi\)
\(600\) 3.46410i 0.141421i
\(601\) 9.50000 + 16.4545i 0.387513 + 0.671192i 0.992114 0.125336i \(-0.0400009\pi\)
−0.604601 + 0.796528i \(0.706668\pi\)
\(602\) 0 0
\(603\) 17.3205i 0.705346i
\(604\) −10.5000 + 6.06218i −0.427239 + 0.246667i
\(605\) 27.7128i 1.12669i
\(606\) 13.5000 7.79423i 0.548400 0.316619i
\(607\) −21.5000 37.2391i −0.872658 1.51149i −0.859237 0.511578i \(-0.829061\pi\)
−0.0134214 0.999910i \(-0.504272\pi\)
\(608\) −4.50000 7.79423i −0.182499 0.316098i
\(609\) 0 0
\(610\) 21.0000 0.850265
\(611\) 7.50000 30.3109i 0.303418 1.22625i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 31.5000 + 18.1865i 1.27227 + 0.734547i 0.975415 0.220375i \(-0.0707280\pi\)
0.296858 + 0.954922i \(0.404061\pi\)
\(614\) 42.0000 1.69498
\(615\) 4.50000 7.79423i 0.181458 0.314294i
\(616\) 0 0
\(617\) 37.5000 + 21.6506i 1.50969 + 0.871622i 0.999936 + 0.0113033i \(0.00359804\pi\)
0.509757 + 0.860318i \(0.329735\pi\)
\(618\) 19.5000 11.2583i 0.784405 0.452876i
\(619\) −16.5000 + 9.52628i −0.663191 + 0.382893i −0.793492 0.608581i \(-0.791739\pi\)
0.130301 + 0.991475i \(0.458406\pi\)
\(620\) 3.00000 0.120483
\(621\) 0 0
\(622\) 22.5000 12.9904i 0.902168 0.520867i
\(623\) 0 0
\(624\) 17.5000 + 4.33013i 0.700561 + 0.173344i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 28.5000 + 16.4545i 1.13909 + 0.657653i
\(627\) 4.50000 7.79423i 0.179713 0.311272i
\(628\) −11.5000 19.9186i −0.458900 0.794838i
\(629\) 0 0
\(630\) 0 0
\(631\) −40.5000 23.3827i −1.61228 0.930850i −0.988841 0.148978i \(-0.952402\pi\)
−0.623439 0.781872i \(-0.714265\pi\)
\(632\) 7.50000 + 4.33013i 0.298334 + 0.172243i
\(633\) 13.0000 0.516704
\(634\) 4.50000 7.79423i 0.178718 0.309548i
\(635\) 22.5167i 0.893546i
\(636\) 9.00000 0.356873
\(637\) 0 0
\(638\) −27.0000 −1.06894
\(639\) 3.46410i 0.137038i
\(640\) −10.5000 + 18.1865i −0.415049 + 0.718886i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) 4.50000 + 2.59808i 0.177463 + 0.102458i 0.586100 0.810239i \(-0.300663\pi\)
−0.408637 + 0.912697i \(0.633996\pi\)
\(644\) 0 0
\(645\) 19.0526i 0.750194i
\(646\) −9.00000 15.5885i −0.354100 0.613320i
\(647\) −4.50000 + 7.79423i −0.176913 + 0.306423i −0.940822 0.338902i \(-0.889945\pi\)
0.763908 + 0.645325i \(0.223278\pi\)
\(648\) −1.50000 0.866025i −0.0589256 0.0340207i
\(649\) 9.00000 15.5885i 0.353281 0.611900i
\(650\) 9.00000 + 8.66025i 0.353009 + 0.339683i
\(651\) 0 0
\(652\) −10.5000 + 6.06218i −0.411212 + 0.237413i
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 9.00000 0.351928
\(655\) −22.5000 + 12.9904i −0.879148 + 0.507576i
\(656\) −22.5000 + 12.9904i −0.878477 + 0.507189i
\(657\) −15.0000 8.66025i −0.585206 0.337869i
\(658\) 0 0
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 9.00000 0.350325
\(661\) −31.5000 18.1865i −1.22521 0.707374i −0.259184 0.965828i \(-0.583454\pi\)
−0.966024 + 0.258454i \(0.916787\pi\)
\(662\) 28.5000 + 49.3634i 1.10768 + 1.91856i
\(663\) 21.0000 + 5.19615i 0.815572 + 0.201802i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.50000 + 0.866025i −0.0580367 + 0.0335075i
\(669\) 5.19615i 0.200895i
\(670\) 22.5000 12.9904i 0.869251 0.501862i
\(671\) 36.3731i 1.40417i
\(672\) 0 0
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 38.1051i 1.46775i
\(675\) 5.00000 + 8.66025i 0.192450 + 0.333333i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) 13.5000 23.3827i 0.518847 0.898670i −0.480913 0.876768i \(-0.659695\pi\)
0.999760 0.0219013i \(-0.00697196\pi\)
\(678\) 22.5000 12.9904i 0.864107 0.498893i
\(679\) 0 0
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) −15.0000 8.66025i −0.574801 0.331862i
\(682\) 15.5885i 0.596913i
\(683\) 24.2487i 0.927851i 0.885874 + 0.463926i \(0.153559\pi\)
−0.885874 + 0.463926i \(0.846441\pi\)
\(684\) −3.00000 1.73205i −0.114708 0.0662266i
\(685\) 0 0
\(686\) 0 0
\(687\) −10.5000 + 6.06218i −0.400600 + 0.231287i
\(688\) 27.5000 47.6314i 1.04843 1.81593i
\(689\) −22.5000 + 23.3827i −0.857182 + 0.890809i
\(690\) 0 0
\(691\) 31.1769i 1.18603i 0.805193 + 0.593013i \(0.202062\pi\)
−0.805193 + 0.593013i \(0.797938\pi\)
\(692\) −7.50000 12.9904i −0.285107 0.493820i
\(693\) 0 0
\(694\) 0 0
\(695\) 19.5000 11.2583i 0.739677 0.427053i
\(696\) 5.19615i 0.196960i
\(697\) −27.0000 + 15.5885i −1.02270 + 0.590455i
\(698\) 4.50000 + 7.79423i 0.170328 + 0.295016i
\(699\) −1.50000 2.59808i −0.0567352 0.0982683i
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 30.0000 8.66025i 1.13228 0.326860i
\(703\) 0 0
\(704\) 4.50000 + 2.59808i 0.169600 + 0.0979187i
\(705\) −15.0000 −0.564933
\(706\) 1.50000 2.59808i 0.0564532 0.0977799i
\(707\) 0 0
\(708\) 3.00000 + 1.73205i 0.112747 + 0.0650945i
\(709\) −10.5000 + 6.06218i −0.394336 + 0.227670i −0.684037 0.729447i \(-0.739777\pi\)
0.289701 + 0.957117i \(0.406444\pi\)
\(710\) 4.50000 2.59808i 0.168882 0.0975041i
\(711\) 10.0000 0.375029
\(712\) 12.0000 0.449719
\(713\) 0 0
\(714\) 0 0
\(715\) −22.5000 + 23.3827i −0.841452 + 0.874463i
\(716\) 1.50000 2.59808i 0.0560576 0.0970947i
\(717\) −9.00000 5.19615i −0.336111 0.194054i
\(718\) 16.5000 28.5788i 0.615775 1.06655i
\(719\) −7.50000 12.9904i −0.279703 0.484459i 0.691608 0.722273i \(-0.256903\pi\)
−0.971311 + 0.237814i \(0.923569\pi\)
\(720\) 17.3205i 0.645497i
\(721\) 0 0
\(722\) −24.0000 13.8564i −0.893188 0.515682i
\(723\) −6.00000 3.46410i −0.223142 0.128831i
\(724\) 2.00000 0.0743294
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 27.7128i 1.02852i
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 25.9808i 0.961591i
\(731\) 33.0000 57.1577i 1.22055 2.11405i
\(732\) 7.00000 0.258727
\(733\) −43.5000 25.1147i −1.60671 0.927634i −0.990100 0.140365i \(-0.955173\pi\)
−0.616609 0.787269i \(-0.711494\pi\)
\(734\) 34.5000 + 19.9186i 1.27342 + 0.735208i
\(735\) 0 0
\(736\) 0 0
\(737\) −22.5000 38.9711i −0.828798 1.43552i
\(738\) −9.00000 + 15.5885i −0.331295 + 0.573819i
\(739\) −34.5000 19.9186i −1.26910 0.732717i −0.294285 0.955718i \(-0.595081\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(740\) 0 0
\(741\) −6.00000 + 1.73205i −0.220416 + 0.0636285i
\(742\) 0 0
\(743\) −1.50000 + 0.866025i −0.0550297 + 0.0317714i −0.527262 0.849703i \(-0.676782\pi\)
0.472233 + 0.881474i \(0.343448\pi\)
\(744\) −3.00000 −0.109985
\(745\) 33.0000 1.20903
\(746\) 28.5000 16.4545i 1.04346 0.602441i
\(747\) 6.00000 3.46410i 0.219529 0.126745i
\(748\) −27.0000 15.5885i −0.987218 0.569970i
\(749\) 0 0
\(750\) 10.5000 18.1865i 0.383406 0.664078i
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 37.5000 + 21.6506i 1.36748 + 0.789517i
\(753\) 1.50000 + 2.59808i 0.0546630 + 0.0946792i
\(754\) 13.5000 + 12.9904i 0.491641 + 0.473082i
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) 8.50000 + 14.7224i 0.308938 + 0.535096i 0.978130 0.207993i \(-0.0666932\pi\)
−0.669193 + 0.743089i \(0.733360\pi\)
\(758\) −1.50000 2.59808i −0.0544825 0.0943664i
\(759\) 0 0
\(760\) 5.19615i 0.188484i
\(761\) −25.5000 + 14.7224i −0.924374 + 0.533688i −0.885028 0.465538i \(-0.845861\pi\)
−0.0393463 + 0.999226i \(0.512528\pi\)
\(762\) 22.5167i 0.815693i
\(763\) 0 0
\(764\) −7.50000 12.9904i −0.271340 0.469975i
\(765\) 20.7846i 0.751469i
\(766\) 13.5000 + 23.3827i 0.487775 + 0.844851i
\(767\) −12.0000 + 3.46410i −0.433295 + 0.125081i
\(768\) −9.50000 + 16.4545i −0.342802 + 0.593750i
\(769\) 16.5000 9.52628i 0.595005 0.343526i −0.172069 0.985085i \(-0.555045\pi\)
0.767074 + 0.641558i \(0.221712\pi\)
\(770\) 0 0
\(771\) 15.0000 25.9808i 0.540212 0.935674i
\(772\) −1.50000 0.866025i −0.0539862 0.0311689i
\(773\) 13.8564i 0.498380i 0.968455 + 0.249190i \(0.0801644\pi\)
−0.968455 + 0.249190i \(0.919836\pi\)
\(774\) 38.1051i 1.36966i
\(775\) −3.00000 1.73205i −0.107763 0.0622171i
\(776\) −4.50000 + 7.79423i −0.161541 + 0.279797i
\(777\) 0 0
\(778\) 4.50000 2.59808i 0.161333 0.0931455i
\(779\) 4.50000 7.79423i 0.161229 0.279257i
\(780\) −4.50000 4.33013i −0.161126 0.155043i
\(781\) −4.50000 7.79423i −0.161023 0.278899i
\(782\) 0 0
\(783\) 7.50000 + 12.9904i 0.268028 + 0.464238i